Daily Practice · Higher Plus
April 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1956 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1956The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2nd April 1956A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 3rd April 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th April 1956A rectangle is 18 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th April 1956Write 2/(x - 6) + 7/(x + 5) as a single fraction.
- 6th April 1956A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 7th April 1956In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 8th April 1956The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 9th April 1956A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 10th April 1956Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 11th April 1956Solve 4x^2 + 8x - 5 = 0.
- 12th April 1956y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 13th April 1956In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 14th April 1956A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 15th April 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th April 1956A block has mass 730 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th April 1956f(x) = 3x - 10. Work out the inverse function f^-1(x).
- 18th April 1956y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 19th April 1956A cuboid measures 8 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th April 1956A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st April 1956A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 22nd April 1956x = 85 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd April 1956Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 24th April 1956y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
- 25th April 1956A cuboid measures 12 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th April 1956A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th April 1956On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th April 1956A car covers 650 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th April 1956Use the iteration x(n+1) = cube root of (7x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 30th April 1956A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.